A photonic integrated circuit is a device that integrates multiple photonic functions for information signals on optical wavelengths typically in the visible spectrum or near infrared 850 nm-1650 nm. Such photonic integrated circuits may include waveguides, beam splitters, beam combiners, phase shifters, photodetectors, amplifiers, and attenuators. Combinations of such optical elements may yield more complex optical elements, including modulators and interferometers (i.e. interference devices). Among various optical elements used in photonic integrated circuits, interferometers are widely used for measurements of small displacements, refractive index changes and other quantities in science and industry. An interferometer includes an optical beam splitter, a section of dissimilar path lengths, and an optical beam combiner. In an interferometer, an incoming light is split into multiple paths by the optical beam splitter (i.e. two or more paths), acquires different phase shifts through the different path lengths, and is re-combined by the optical beam combiner.
In particular, multi-mode interference (MMI) devices may provide beam splitters and beam combiners, and therefore may be included as elements of an interferometer. While most waveguides in photonic integrated circuits may be designed for a single mode propagation, MMI devices operate using a large number of modes.
Typically, a MMI device is fabricated as a simple wide rectangular stripe in a 2-dimensional flat plane and behaves as a multi-mode waveguide. In such a MMI device, an incoming optical information signal (used interchangeably herein with “light”) of a certain transverse optical profile (i.e. the intensity of the incoming light varies in a direction transverse to the propagation direction) simultaneously excites multiple modes at an input face of the MMI device with different amplitudes which then propagate at different phase velocities. In the paraxial regime (i.e. an angle between an incoming light and the propagation direction always remains smaller than about 20 degrees), after a certain propagation distance, the modes excited at the input face are recombined in-phase such that they reproduce the optical transverse profile of the incoming light at the input face. This phenomenon is referred to as self-imaging. Furthermore, such self-imaging occurs at multiple-locations (referred herein to as “self-imaging points”) during the propagation and allows a MMI device to split an incoming light into two or more reproductions of the incoming light at an output face of the MMI device. In particular, most MMI devices are designed to provide multiple reproductions of an incoming light at the output face with nearly equal intensities. In such a MMI device, output ports may be placed at self-imaging points, where the MMI device may act as a beam splitter. A MMI device, with two input ports for two incoming light beams, may act as a beam combiner.
Although single-mode waveguides are often used in integrated circuits, it is of a common use to provide adiabatic tapers as the input waveguides that bring the optical signal up to the input face of the MMI. In such a taper, the waveguide is single-mode at its input and becomes gradually multi-mode as its width increases towards the input face of the MMI. Providing small width single-mode waveguides up to the MMI input would cause strong divergence of the light inside the MMI. Increasing the size of the optical profile at the input face of the MMI device, through the use of tapers, allows to mitigate such diffraction and to remain closer to the paraxial regime.
A Mach-Zehnder type interferometer may be constructed by a combination of MMI devices, including a 1×2 MMI device (with one input port and two output ports, as a beam splitter) and a 2×2 MMI device (with two input ports and two output ports, as a beam combiner). An incoming light is split into two light beams by the 1×2 MMI device (beam splitter). Those light beams propagate in two separate paths (used interchangeably here in with “arms”) towards the 2×2 MMI device (beam combiner). Since the two paths may have different lengths, the light beams propagating through the two paths experience different phase shifts, proportional to a difference between length of the two paths. Subsequently, the light beams enter the 2×2 MMI device (beam combiner). The output power of the 2×2 MMI device (beam combiner) vary in a wave pattern as a function of a phase shift difference, as a typical of a two-arms interferometer.
An optical hybrid interferometer may also be constructed by a combination of MMI devices, including a 2×4 MMI device (with two input ports and four outputs) and a 2×2 MMI device (with two input ports and two output ports). The 2×4 MMI device may be in the so-called paired-interference configuration. Two of the output ports of the 2×4 MMI device are connected to the two input ports of the 2×2 MMI device via two arms, respectively, which have different lengths as discussed previously. Such combination of MMI devices provides the functionality of a 90-degree optical hybrid as long as the phase shift of the bottom arm exceeds the phase shift of the upper arm by 45 degrees, as is known in the art.
For the interferometers with separate arms, as discussed above, their proper operation critically depends on the accuracy of a phase shift difference Δφ, between the two arms connecting the MMI devices, specifically only on Δφ, instead of a phase shift of φ in one arm or one of φ+Δφ in the other arm. However, for robustness of fabricated interferometer devises, the arms are commonly designed as short as possible (and accordingly a common phase shift value φ as small as possible). In an interferometer device with long arms, small deviations in any characteristics in the device may result in substantial errors in the phase shift difference Δφ. Therefore, the device may not function as designed in conventional designs of interferometers with separate arms.